Author

Kyle Luh

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Preprint Oct 2026

Universality for the extreme eigenvalues of Laplacian random matrices

We study the eigenvalues of the random Laplacian matrix $D - A$, where $A$ is a Wigner matrix with sub-Gaussian entries and the diagonal matrix $D$ contains the row sums of $A$. Our main results show that the extreme eigenvalues of this model exhibit Poisson statistics; in particular, after the appropriate centering an...

A. Campbell, Kyle Luh, Sean O'Rourke · 0 citations

Preprint Sep 2026

Linear Independence of Random Boolean Tensor Powers at the Dimension Threshold

Let $d \geq 1$ be fixed and let \[ D(n,d) := \sum_{j=0}^{d} \binom{n-1}{j}. \] We show that if $x^{(1)}, \dots, x^{(m)}$ are independent uniform points of $\{\pm 1\}^n$ then uniformly for $m \leq D(n,d)$, there exists a constant $C_d>0$ such that \[ \mathbb{P}((x^{(1)})^{\otimes d}, \dots, (x^{(m)})^{\otimes d} \text{...

Kyle Luh · 0 citations